Answer:
See below.
Step-by-step explanation:
The sum of the exterior angles of any convex polygon is 360 degrees.
Therefore for a regular polygon n * E = 360 where n = the number of sides in the polygon , n is an integer greater than 2 and E = value of each exterior angle.
Answers:
Exterior angle = 90, 90 * 4 = 360 so this polygon has 4 sides.
80 degrees: n * 80 = 360, n = 4.5 so this angle is not possible.
75 degrees: n * 75 = 360, n = 4.8 so this is not possible.
30 degrees: n * 30 = 360 , n = 12 so this has 12 sides.
46 degrees: n * 46 = 360, n = 7.8 so this is not possible.
36 degrees: n * 36 = 360, n = 10 so this has 12 sides.
2 degrees: n * 2 = 360, n = 180, so this has 180 sides.
